THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Bo Xu

,

Pengchao Shi

,

Sheng Zhang

NON-DIFFERENTIABLE FRACTIONAL ODD-SOLITON SOLUTIONS OF LOCAL FRACTIONAL GENERALIZED BROER-KAUP SYSTEM BY EXTENDING DARBOUX TRANSFORMATION

ABSTRACT
In this paper, a local fractional generalized Broer-Kaup (gBK) system is first de­rived from the linear matrix problem equipped with local space and time fractional partial derivatives, i.e, fractional Lax pair. Based on the derived fractional Lax pair, the second kind of fractional Darboux transformation (DT) mapping the old potentials of the local fractional gBK system into new ones is then established. Finally, non-differentiable frcational odd-soliton solutions of the local fractional gBK system are obtained by using two basic solutions of the derived fractional Lax pair and the established fractional DT. This paper shows that the DT can be extended to construct non-differentiable fractional soliton solutions of some local fractional non-linear evolution equations in mathematical physics.
KEYWORDS
non-differentiable fractional odd-soliton solution, fractional Lax pair, second kind of fractional DT, local fractional gBK system
PAPER SUBMITTED: 2022-05-01
PAPER REVISED: 2022-06-04
PAPER ACCEPTED: 2022-06-14
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1077X
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [77 - 86]
REFERENCES
  1. Fan, J., Liu, Y., Heat Transfer in the Fractal Channel Network of Wool Fiber, Materials Science and Technology, 26 (2010), 11, pp. 1320-1322
  2. Fan, J., Shang, X. M., Fractal Heat Transfer in Wool Fiber Hierarchy, Heat Transfer Research, 44 (2013), 5, pp. 399-407
  3. Fan, J., et al., Influence of Hierarchic Structure on the Moisture Permeability of Biomimic Woven Fabricusing Fractal Derivative Method, Advances in Mathematical Physics, 2015 (2015), Apr., ID817437
  4. He, J. H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  5. He, J, H., Fractal Calculus and its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
  6. He, J. H., A New Fractal Derivation, Thermal Science, 15 (2011), Suppl. 1, pp. S145-S147
  7. Khalil, R., et al., A New Definition of Fractional Derivative, Journal of Computational and Applied Mathematics, 264 (2014), July, pp. 65-70
  8. Xu, B., et al., Analytical Methods for Non-linear Fractional Kolmogorov-Petrovskii-Piskunov Equation: Soliton Solution and Operator Solution, Thermal Science, 25 (2021), 3B, pp. 2159-2166
  9. Xu, B., et al., Line Soliton Interactions for Shallow Ocean-Waves and Novel Solutions with Peakon, Ring, Conical, Columnar and Lump Structures Based on Fractional KP Equation, Advances in Mathematical Physics, 2021 (2021), ID6664039
  10. Zhang, S., et al., Variable Separation for Time Fractional Advection-Dispersion Equation with Initial and Boundary Conditions, Thermal Science, 20 (2016), 3, pp. 789-792
  11. Xu, B., et al., Variational Iteration Method for Two Fractional Systems with Boundary Conditions, Thermal Science, 26 (2022), 3B, pp. 2649-2657
  12. Xu, B., et al., Fractional Isospectral and Non-isospectral AKNS Hierarchies and Their Analytic Methods for N-fractal Solutions with Mittag-Leffler Functions, Advances in Difference Equations, 2021 (2021), ID223
  13. Xu, B., et al., Fractional Rogue Waves with Translational Coordination, Steep Crest and Modified Asymmetry, Complexity, 2021, (2021), ID6669087
  14. Xu, B., Zhang, S., Riemann-Hilbert Approach for Constructing Analytical Solutions and Conservation Laws of a Local Time-Fractional Non-linear Schrödinger Equation, Symmetry, 13 (2021), 9, ID13091593
  15. Zhang, S., Zheng, X. W., Non-Differentiable Solutions for Non-linear Local Fractional Heat Conduction Equation, Thermal Science, 25 (2021), Special Issue 2, S309-S314
  16. Hristov, J., Transient Heat Diffusion with a Non-singular Fading Memory from the Cattaneo Constitutive Equation with Jeffrey's Kernel to the Caputo-Fabrizio Time-Fractional Derivative, Thermal Science, 20 (2016), 2, pp. 757-762
  17. Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, London, UK, 2015
  18. Zhang, Y. F., et al., An Integrable Hierachy and Darboux Transformations, Bilinear Backlund Transformations of a Reduced Equation, Applied Mathematics and Computation, 219 (2013), 11, pp. 5837-5848
  19. Zhang, S., Liu, D. D., The Third Kind of Darboux Transformation and Multisoliton Solutions for Generalized Broer-Kaup Equations, Turkish Journal of Physics, 39 (2015), 2, pp. 165-177
  20. Zhang, S., Zheng, X. W., N-Soliton Solutions and Non-linear Dynamics for Two Generalized Broer-Kaup Systems, Non-Linear Dynamics, 107 (2022), Jan., pp. 1179-1193
  21. Zhang, S., Xu, B., Painleve Test and Exact Solutions for (1+1)-Dimensional Generalized Broer-Kaup Equations, Mathematics, 10 (2022), 3, ID 486
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Non-differentiable fractional odd-soliton solutions of local fractional generalized Broer-Kaup system by extending Darboux transformation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence